Parameter estimation for partially observed queues

Author

Chen, Thomas M. ; Walrand, Jean ; Messerschmitt, David G.

Author_Institution

GTE Labs. Inc., Waltham, MA, USA

Volume

42

Issue

9

fYear

1994

fDate

9/1/1994 12:00:00 AM

Firstpage

2730

Lastpage

2739

Abstract

We consider parameter estimation for a FIFO queue with deterministic service times and two independent arrival streams of “observed” and “unobserved” packets. The arrivals of unobserved packets are Poisson with an unknown rate λ while the arrivals of observed packets are arbitrary. Maximum likelihood estimation of λ is formulated based on the arrival times and waiting times of k observed packets. The likelihood function is derived in terms of the transition probabilities of the unfinished work process which are calculated recursively. Sufficient conditions for consistency, asymptotic normality, and asymptotic efficiency are given. The mean and variance of the MLE are measured in simulation experiments. Numerical results indicate that the MLE is consistent and asymptotically normal

Keywords

maximum likelihood estimation; packet switching; parameter estimation; probability; queueing theory; FIFO queue; MLE; Poisson arrivals; arrival times; asymptotic efficiency; asymptotic normality; consistency; deterministic service times; independent arrival streams; likelihood function; maximum likelihood estimation; mean; observed packets; parameter estimation; partially observed queues; simulation experiments; sufficient conditions; transition probabilities; unfinished work process; unobserved packets; variance; waiting times; Asynchronous transfer mode; Computer networks; Delay estimation; Length measurement; Maximum likelihood estimation; Packet switching; Parameter estimation; Performance evaluation; Probability; Speech;

fLanguage

English

Journal_Title

Communications, IEEE Transactions on

Publisher

ieee

ISSN

0090-6778

Type

jour

DOI

10.1109/26.317414

Filename

317414